Infrared reflectivity versus doping in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ and ${\mathrm{Nd}}_{1+\mathit{y}}$${\mathrm{Ba}}_{2\mathrm{-}\mathit{y}}$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ ceramics: Relationship with the t-J model

We have measured the room-temperature reflectivity spectra in the infrared and visible range (500–25 000 ${\mathrm{cm}}^{\mathrm{-}1}$) of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ (0≤x≤1) and ${\mathrm{Nd}}_{1+\mathit{y}}$ ${\mathrm{Ba}}_{2\mathrm{-}\mathit{y}}$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ (0≤y≤0.5) polished ceramics as a function of doping (x and y). We show that the intensity of the entire infrared spectrum increases with the hole doping level (x or y). When separated into a Drude contribution and a mid-infrared band, both contributions exhibit a correlated increase as holes are transferred into the conducting ${\mathrm{CuO}}_2$ planes and are therefore argued to be related to free carriers. We note that recent simulations of the t-J model, studied as a function of hole doping, provide a consistent description of such a behavior.